A385507 a(n) = v(1 + F(2*n - 1)), where F(x) = (3*x + 1)/2^v(3*x + 1), x is any odd natural number, and v(y) is the 2-adic valuation of y.
1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 1, 2, 2, 1, 2, 4, 1, 1, 3, 2, 5, 1, 1, 3, 1, 1, 1, 2, 2, 1, 3, 5, 1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 1, 2, 2, 1, 2, 4, 1, 1, 2, 2, 4, 1, 1, 3, 1, 1, 2, 2, 2, 1, 4, 6, 1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 3, 2, 2, 1, 2, 4
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
v[y_] := IntegerExponent[y, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; Table[v[1 + f[2*k -1]], {k, 73}] -
PARI
F(x) = (3*x + 1)/2^valuation(3*x + 1, 2); a(n) = valuation(1 + F(2*n - 1), 2); \\ Michel Marcus, Jul 01 2025
Formula
a(2n) = A001511(n).
a(4n-3) = A001511(3n-2).
a(4n-1) = a(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Jul 23 2025